Singlet Transducer

A transducer emitting a single output tape, i.e. the trivial single-sequence instance of a string transducer that is equivalent to an HMM with one output and only one emitting state.
See Transducer Legend for key to diagram.

Probabilistic constraints:

g + h = 1.

Note the built-in S/I symmetry of this model.

We can write this as
denoting the replacement of an empty (dummy) input sequence with a possibly nonempty output sequence which occurs if the reversible evolutionary process is allowed to run forever
(compare with the symbol for the Gotoh Transducer which represents a finite time interval ).